Question 1 of 10

Hamsters can have a variety of colors, including golden and black. The allele for golden color [tex]\((G)\)[/tex] is dominant over the allele for black color [tex]\((g)\)[/tex]. The table shows the genotypes and phenotypes for a small population of hamsters.

[tex]\[
\begin{tabular}{|l|l|l|}
\hline
Genotype & Phenotype & Number of hamsters \\
\hline
GG & Golden & 12 \\
\hline
Gg & Golden & 25 \\
\hline
gg & Black & 13 \\
\hline
\end{tabular}
\][/tex]

What is the frequency of the black phenotype?

A. [tex]\(\frac{12}{50}\)[/tex]

B. [tex]\(\frac{13}{50}\)[/tex]

C. [tex]\(\frac{13}{38}\)[/tex]

D. [tex]\(\frac{25}{25}\)[/tex]



Answer :

To determine the frequency of the black phenotype in the hamster population, follow these steps:

1. Identify the total number of hamsters in the population:
- Golden hamsters with genotype [tex]\(GG\)[/tex]: 12
- Golden hamsters with genotype [tex]\(Gg\)[/tex]: 25
- Black hamsters with genotype [tex]\(gg\)[/tex]: 13

Add these numbers together:
[tex]\[ \text{Total number of hamsters} = 12 + 25 + 13 = 50 \][/tex]

2. Determine the number of black hamsters with genotype [tex]\(gg\)[/tex]:
- From the table, we know there are 13 black hamsters.

3. Calculate the frequency of the black phenotype:
- Frequency is given by the ratio of the number of black hamsters to the total number of hamsters.
[tex]\[ \text{Frequency of black phenotype} = \frac{\text{Number of black hamsters}}{\text{Total number of hamsters}} = \frac{13}{50} \][/tex]

4. Simplify the fraction (if necessary) and convert to decimal form:
- In this case, [tex]\(\frac{13}{50}\)[/tex] is already in its simplest form and converts to [tex]\(0.26\)[/tex].

Thus, the frequency of the black phenotype is [tex]\( \frac{13}{50} \)[/tex], which corresponds to option B.